Orthogonal frequency-division multiplexing (OFDM) offers the advantages of improved downlink system capacity, coverage and data rates for packet data services with high spectral efficiency due to a nearly rectangular spectrum occupancy, and low-cost implementation using the Fast Fourier Transform (FFT). OFDM has been exploited for wideband data communications over mobile radio channels, high bit rate digital subscriber lines (HDSLs), asymmetric digital subscriber lines (ADSLs), and digital broadcasting. OFDM partitions the entire bandwidth into parallel independent subcarriers to transmit parallel data streams. The relative longer symbol duration and guard interval provide great immunity to intersymbol interference (ISI). Recently it received considerable attention as an air interface for evolution of UMTS mobile radio systems in 3GPP standardization forum.
A conventional OFDM transceiver is shown in FIG. 1. As shown in FIG. 1, the information bits are encoded, rate-matched and modulated based on adaptive modulation and coding (AMC) set. Then the signal is processed by the N-point IFFT such as
                                                                        b                ⁡                                  (                  n                  )                                            =                                                IFFT                  ⁢                                      {                                          B                      ⁡                                              (                        k                        )                                                              }                                                  =                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            B                      ⁡                                              (                        k                        )                                                              ⁢                                                                                  ⁢                                          exp                      ⁡                                              (                                                  j                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          k                          ⁢                                                                                                          ⁢                                                      n                            /                            N                                                                          )                                                                                                                                                                                    n                =                0                            ,              1              ,              2              ,              …              ⁢                                                          ,                              N                -                1                                                                        (        1        )            where B(k) is the data sequence of length N. Then the output of IFFT is converted from parallel to serial (P/S), and inserted by the redundancy in the form of a guard interval (GI) of length greater than maximum delay spread such as
                              x          ⁡                      (            n            )                          =                  {                                                                                          b                    ⁡                                          (                                              N                        +                        n                                            )                                                        ,                                                                                                  n                    =                                          -                      G                                                        ,                                                            -                      G                                        +                    1                                    ,                  …                  ⁢                                                                          ,                                      -                    1                                                                                                                                            b                    ⁡                                          (                      n                      )                                                        ,                                                                                                  n                    =                    0                                    ,                  1                  ,                  2                  ,                  …                  ⁢                                                                          ,                                      N                    -                    1                                                                                                          (        2        )            where x(n) is the transmitted signals, G is the GI length. Finally, GI-added IFFT output x(n) is up-converted at the carrier frequency and transmitted over the frequency-selective fading channel with additive white Gaussian noise (AWGN).
The received signal at the UE is given byr(t)=h(t){circle around (X)}x(t)+n(t)  (3)where {circle around (X)} denotes the convolution operation,
                              h          ⁡                      (            t            )                          =                              ∑            l            L                    ⁢                                                    a                l                            ⁡                              (                t                )                                      ⁢                                                  ⁢                          δ              ⁡                              (                                  t                  -                                      τ                    l                                                  )                                                                        (        4        )            is the channel impulse response in time domain, L is the number of paths, al(t) is the complex channel coefficient at the lth path, τl is the tap delay, δ(t) is the delta function, n(t) is the additive white Gaussian noise. The GI is removed from the received signal and the GI-removed signal is processed by FFT as follows
                                                                                          y                  ⁡                                      (                    n                    )                                                  =                                  r                  ⁡                                      (                                          n                      +                      G                                        )                                                              ,                                                                          n                =                0                            ,              1              ,              2              ,              …              ⁢                                                          ,                              N                -                1                                                                        (        5        )                                          Y          ⁡                      (            k            )                          =                              FFT            ⁢                          {                              y                ⁡                                  (                  n                  )                                            }                                =                                    1              N                        ⁢                                                  ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                y                  ⁡                                      (                    n                    )                                                  ⁢                                                                  ⁢                                  exp                  ⁡                                      (                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      k                      ⁢                                                                                          ⁢                                              n                        /                        N                                                              )                                                                                                          (        6        )                                          k          =          0                ,        1        ,        2        ,        …        ⁢                                  ,                  N          -          1                                                
If the bandwidth of each subcarrier is much less than the channel coherence bandwidth, a frequency flat channel model can be assumed at each subcarrier so that only a one-tap equalizer is needed for each subcarrier at the receiver. With the channel estimates in frequency domain H(k), the received signal can be equalized by zero-forcing detector such as
                                                                                          B                  ^                                ⁡                                  (                  k                  )                                            =                                                                                          (                                              H                        ⁡                                                  (                          k                          )                                                                    )                                                              -                      1                                                        ⁢                                      Y                    ⁡                                          (                      k                      )                                                                      =                                                                                                    H                        *                                            ⁡                                              (                        k                        )                                                              ⁢                                                                                  ⁢                                          Y                      ⁡                                              (                        k                        )                                                                                                                                                                      H                        ⁡                                                  (                          k                          )                                                                                                            2                                                                                                                          k                =                0                            ,              1              ,              2              ,              …              ⁢                                                          ,                              N                -                1                                                                        (        7        )            or in minimum mean square error (MMSE) criteria such as
                                                                                          B                  ^                                ⁡                                  (                  k                  )                                            =                                                                                          H                      *                                        ⁡                                          (                      k                      )                                                        ⁢                                                                          ⁢                                      Y                    ⁡                                          (                      k                      )                                                                                                                                                                                H                        ⁡                                                  (                          k                          )                                                                                                            2                                    +                                      σ                    2                                                                                                                          k                =                0                            ,              1              ,              2              ,              …              ⁢                                                          ,                              N                -                1                                                                        (        8        )            where ( )* and ∥2 denote the complex conjugate operation and power respectively, σ2 is the noise variance. Then the equalized signal is demodulated, rate matched and decoded correspondingly.
The corresponding discrete-time received signal with GI removal is
                                                        y              =                                                                    THGF                                          -                      1                                                        ⁢                  b                                +                n                                                                                        =                                                                    XF                                          -                      1                                                        ⁢                  b                                +                n                                                                        (        9        )            where y is the received signal vector, T is the truncating matrix, H is the matrix with channel impulse response, G is the matrix for GI inserting, F−1 is the IFFT matrix, b is the vector of transmitted symbols and n is the noise vector. Assuming the GI length is greater than maximum delay spread, x=THG is the circular square matrix and can be modeled asX=F−1HfF  (10)where Hf is the diagonal matrix with channel impulse response in frequency domain, and F is the FFT matrix. Then the received signal with GI removal in Eq. 9 can be simplified intoy=F−1Hfb+n  (11)The transmitted signal can be detected by FFT and one-tap zero-forcing channel equalizer such as{circumflex over (b)}=(Hf)−1Fy  (12)or in MMSE such as
                              b          ^                =                                                            (                                  H                  f                                )                            *                        ⁢            Fy                                                                                                H                  f                                                            2                        +                          σ              2                                                          (        13        )            
Frequency hopping has been proposed for reuse-one OFDM systems, which enables a full frequency reuse across the neighboring cells, provides frequency diversity by interleaving and spreading the transmitted subcarriers over the whole bandwidth, and averages the intercell interference as well. However, frequency hopping makes the reuse-one OFDM system not as efficient in spectrum efficiency as in WCDMA. The subset of subcarriers are used by the specific UE implies for lower peak data rate. Additionally, it is also a challenge for radio network control for resource and sub-carrier allocation. OFDM channel mapping has been proposed without requiring resource planning on network level by modeling the time-frequency pattern using normalized a periodic Hamming auto-correlation function. However, it is not a spectrum effective scheme either.
Selective scrambling in frequency domain has been proposed for OFDM to reduce the peak to average power ratio (PAR) (see Yang et al. “Peak-to-Average Power Control in OFDM Using Standard Arrays of Linear Block Codes” IEEE Commun. Letters, vol. 7, No. 4, pp. 174-176, April 2003; Eetvelt et al. “Peak-to-Average Power Reduction for OFDM Schemes by Selective Scrambling”, IEE Electronics Letters, Vol. 32, No. 21, pp. 1963-1964, October 1996). A cell specific code has been proposed to scramble the signals in frequency domain for fast cell search in orthogonal frequency and code division multiplexing (OFCDM) and multicarrier CDMA systems (see Tanno et al. “Three-Step Fast Cell Search Algorithm Utilizing Common Pilot Channel for OFDM Broadband Packet Wireless Access” IEE VTC-Fall, Vol, 3, pp. 24-28, 2002; Hanada et al. “Three-Step Cell Search Algorithm for Broadband Multi-carrier CDMA Packet Wireless Access”, IEEE PIMRC, Vol. 2, pp. G32-37, 2001). A pseudo-noise (PN) code scrambling in time domain has been also applied for user separation in OFDM-CDMA system (see Kim et al., “An OFDM-CDMA Scheme Using Orthogonal Code Multiplexing and Its Parallel Interference Cancellation Receiver”, IEEE ISSSTA, pp. 368-372, Czech Rep. September 2002). However, the scrambling in frequency domain cannot suppress the interference impact induced by neighboring cells for reuse-one OFDM systems.